Overlapped

1
Prolog to an Internet link ...
A generic NCO - based open - loop DDS system
ACRONYMS DDS Direct Digital Synthesis NCO
Numerically Controlled Oscillator ACC
accumulator LUT Look-Up Table DAC
Digital-to-Analog Converter AIF
Anti-Imaging Filter reg register gcd
greatest common divisor PT Phase
Truncation AQ Amplitude Quantization FFT
Fast Fourier Transform FPGA Field
Programmable Gate Array DDC Digital Down
Converter DUC Digital Up Converter SDR
Software Defined Radio ARB arbitrary
r phase ACC register length ( frequency
resolution ) m memory (LUT) address length (
phase resolution ) n data width ( amplitude
resolution)
numerical frequency
Spurious spectral components due to
finite word length effects
Spectral purity is one of the most important
specifications to the signal synthesis.
Overlapped modulation structure
Overlapped harmonic structure
There is a simple procedure for evaluating the
spur structures due to numerical distortion in a
single-tone DDS.
PT - spurs
AQ - spurs
r 11, m 7, without AQ, D 150
Determining the location and the level of
spurs is a good starting point for the NCO
design or selection ( e.g. parameterization of an
NCO core in FPGA ).
r 10, m 10 n 12, D 32
In digital communication systems there are
several applications that do not convert the
numerical samples into an analog signal
digital radios and modems,
software-defined radios, digital
down/up converters.
P 2r / gcd(D, 2r) 32 ( sample period ) No.
of the AQ-spurs (P/4) - 1 7
E 2r-m / gcd(D, 2r-m) 8 ( period of the
phase error ) No. of the PT-spurs E - 1 7
r 11, m 7, with AQ n 12, D 150
r 10, with PT m 7, n 12, D 32
Interactive simulation helps to discover the
composed spectral maps for specific
applications and tuning ranges ( spurs vary
rather irregularly with tuning ), proves to
be a usable tool for multi-tone ( DDS-based
ARB waveform generators ).
Same as above, i.e. there are no PT -
spurs because E 1 at the specific
D tuning word
An example of multi-tone
No. of the AQ-spurs (P/4) - 1 255
An example of interaction between PT and AQ
harmonically related cos components with -5dB
level change (and 8K FFT, BH7 window)
zero-phase sine, 8K FFT, BH7 (7-term
Blackman-Harris) window, without and with AQ
( D is all two in hexa, E 65 536 )
( P 2 147 483 648 )
Online interactive ( Mathcad ) simulations and
movie clips http//www.hit.bme.hu/people/pa
pay/sci/DDS/simul.htm
email papay_at_hit.bme.hu